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E = | F q | = k | qQ qr 2 | = k | Q | r 2 . size 12{E= { {F} over {q} } =k { { ital "qQ"} over { ital "qr" rSup { size 8{2} } } } =k { {Q} over {r rSup { size 8{2} } } } } {}

Since the test charge cancels, we see that

E = k | Q | r 2 . size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {}

The electric field is thus seen to depend only on the charge Q size 12{Q} {} and the distance r size 12{r} {} ; it is completely independent of the test charge q size 12{q} {} .

Calculating the electric field of a point charge

Calculate the strength and direction of the electric field E size 12{E} {} due to a point charge of 2.00 nC (nano-Coulombs) at a distance of 5.00 mm from the charge.

Strategy

We can find the electric field created by a point charge by using the equation E = kQ / r 2 size 12{E= { ital "kQ"} slash {r rSup { size 8{2} } } } {} .

Solution

Here Q = 2 . 00 × 10 9 size 12{Q=2 "." "00" times "10" rSup { size 8{ - 9} } } {} C and r = 5 . 00 × 10 3 size 12{r=5 "." "00" times "10" rSup { size 8{ - 3} } } {} m. Entering those values into the above equation gives

E = k Q r 2 = ( 8.99 × 10 9 N m 2 /C 2 ) × ( 2.00 × 10 9 C ) ( 5.00 × 10 3 m ) 2 = 7.19 × 10 5 N/C. alignl { stack { size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {} #= \( 9 "." "00" times "10" rSup { size 8{9} } N cdot m rSup { size 8{2} } "/C" rSup { size 8{2} } \) times { { \( 2 "." "00" times "10" rSup { size 8{ - 9} } C \) } over { \( 5 "." "00" times "10" rSup { size 8{ - 3} } m \) rSup { size 8{2} } } } {} # =7 "." "20" times "10" rSup { size 8{5} } "N/C" {}} } {}

Discussion

This electric field strength is the same at any point 5.00 mm away from the charge Q size 12{Q} {} that creates the field. It is positive, meaning that it has a direction pointing away from the charge Q size 12{Q} {} .

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Calculating the force exerted on a point charge by an electric field

What force does the electric field found in the previous example exert on a point charge of –0.250 μ C ?

Strategy

Since we know the electric field strength and the charge in the field, the force on that charge can be calculated using the definition of electric field E = F / q size 12{E= {F} slash {q} } {} rearranged to F = q E size 12{F= ital "qE"} {} .

Solution

The magnitude of the force on a charge q = 0 . 250 μC size 12{q= - 0 "." "250""μC"} {} exerted by a field of strength E = 7 . 20 × 10 5 size 12{E=7 "." "20" times "10" rSup { size 8{5} } } {} N/C is thus,

F = qE = ( 0.250 × 10 –6 C ) ( 7.20 × 10 5 N/C ) = 0.180 N. alignl { stack { size 12{F= ital "qE"} {} #size 12{ {}= \( "-0" "." "250" times "10" rSup { size 8{"-6"} } `C \) \( 7 "." "20" times "10" rSup { size 8{5} } `"N/C" \) } {} # ="-0" "." "180"`N {}} } {}

Because q is negative, the force is directed opposite to the direction of the field.

Discussion

The force is attractive, as expected for unlike charges. (The field was created by a positive charge and here acts on a negative charge.) The charges in this example are typical of common static electricity, and the modest attractive force obtained is similar to forces experienced in static cling and similar situations.

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Phet explorations: electric field of dreams

Play ball! Add charges to the Field of Dreams and see how they react to the electric field. Turn on a background electric field and adjust the direction and magnitude.

Electric Field of Dreams

Section summary

  • The electrostatic force field surrounding a charged object extends out into space in all directions.
  • The electrostatic force exerted by a point charge on a test charge at a distance r size 12{r} {} depends on the charge of both charges, as well as the distance between the two.
  • The electric field E size 12{E} {} is defined to be
    E = F q , size 12{E= { {F} over {q,} } } {}

    where F size 12{F} {} is the Coulomb or electrostatic force exerted on a small positive test charge q size 12{q} {} . E size 12{E} {} has units of N/C.

  • The magnitude of the electric field E size 12{E} {} created by a point charge Q size 12{Q} {} is
    E = k | Q | r 2 . size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {}

    where r size 12{r} {} is the distance from Q size 12{Q} {} . The electric field E size 12{E} {} is a vector and fields due to multiple charges add like vectors.

Conceptual questions

Why must the test charge q size 12{q} {} in the definition of the electric field be vanishingly small?

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Are the direction and magnitude of the Coulomb force unique at a given point in space? What about the electric field?

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Problem exercises

What is the magnitude and direction of an electric field that exerts a 2 . 00 × 10 - 5 N size 12{2 "." "00" times "10" rSup { size 8{5} } N} {} upward force on a –1.75 μ C charge?

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What is the magnitude and direction of the force exerted on a 3.50 μ C charge by a 250 N/C electric field that points due east?

8 . 75 × 10 4 size 12{8 "." "75" times "10" rSup { size 8{ - 4} } } {} N

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Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC (such as found on the terminal of a Van de Graaff).

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(a) What magnitude point charge creates a 10,000 N/C electric field at a distance of 0.250 m? (b) How large is the field at 10.0 m?

(a) 6 . 94 × 10 8 C size 12{ {underline {6 "." "94" times "10" rSup { size 8{ - 8} } " C"}} } {}

(b) 6 . 25 N/C size 12{ {underline {6 "." "25"" N/C"}} } {}

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Calculate the initial (from rest) acceleration of a proton in a 5 . 00 × 10 6 N/C size 12{5 "." "00" times "10" rSup { size 8{6} } "N/C"} {} electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.

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(a) Find the direction and magnitude of an electric field that exerts a 4 . 80 × 10 17 N size 12{4 "." "80" times "10" rSup { size 8{ - "17"} } N} {} westward force on an electron. (b) What magnitude and direction force does this field exert on a proton?

(a) 300 N/C ( east ) size 12{ {underline {"300"" N/C " \( "eas"}} {underline {t \) }} } {}

(b) 4 . 80 × 10 17 N ( east ) size 12{ {underline {4 "." "80" times "10" rSup { size 8{ - "17"} } " N " \( "east" \) }} } {}

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Questions & Answers

why static friction is greater than Kinetic friction
Ali Reply
draw magnetic field pattern for two wire carrying current in the same direction
Ven Reply
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
MAHADEV
sorry..E and R are non zero...
MAHADEV
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
Elene Reply
what Is linear momentum
Victoria Reply
why no diagrams
Blessing Reply
where
Fayyaz
Myanmar
Pyae
hi
Iroko
hello
Abdu
Describe an experiment to determine short half life
Tyson Reply
what is science
Kenedy Reply
it's a natural phenomena
Hassan
sap
Emmanuel
please can someone help me with explanations of wave
Benedine
there are seven basic type of wave radio waves, gyamma rays (nuclear energy), microwave,etc you can also search 🔍 on Google :-)
Shravasti
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
what is physics
Caya Reply
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
Magret Reply
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
fundamental quantities are, length , mass, time, current, luminous intensity, amount of substance, thermodynamic temperature.
Shravasti
fundamental quantities are quantities that are independent of others and cannot be define in terms of other quantities there is nothing like Qualities we have only fundamental quantities which includes; length,mass,time, electric current, luminous density, temperature, amount of substance etc
Gift
give examples of three dimensional frame of reference
Ekwunazor Reply
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
Lathan Reply
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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